Utility of the Nudged Elastic Band Method in Identifying the Minimum Energy Path of an Elementary Organometallic Reaction Step

Nudged Elastic Band Method for Molecular Reactions Using Energy-Weighted Springs Combined with Eigenvector Following

The climbing image nudged elastic band method (CI-NEB) is used to identify reaction coordinates and to find saddle points representing transition states of reactions. It can make efficient use of parallel computing as the calculations of the discretization points, the so-called images, can be carried out simultaneously. In typical implementations, the images are distributed evenly along the path by connecting adjacent images with equally stiff springs. However, for systems with a high degree of flexibility, this can lead to poor resolution near the saddle point. By making the spring constants increase with energy, the resolution near the saddle point is improved. To assess the performance of this energy-weighted CI-NEB method, calculations are carried out for a benchmark set of 121 molecular reactions. The performance of the method is analyzed with respect to the input parameters. Energy-weighted springs are found to greatly improve performance and result in successful location of the saddle points in less than a thousand energy and force evaluations on average (about a hundred per image) using the same set of parameter values for all of the reactions. Even better performance is obtained by stopping the calculation before full convergence and complete the saddle point search using an eigenvector following method starting from the location of the climbing image. This combination of methods, referred to as NEB-TS, turns out to be robust and highly efficient as it reduces the average number of energy and force evaluations down to a third, to 305. An efficient and flexible implementation of these methods has been made available in the ORCA software.

Theoretical Probe to the Mechanism of Pt-Catalyzed C-H Acylation Reaction: Possible Pathways for the Acylation Reaction of a Platinacycle

Density functional theory (DFT) and nudged elastic band (NEB) theory have been used to study the possible pathways for the acylation of cycloplatinated complex A derived from 2-phenoxypyridine, which is conceived as the key step in the platinum-catalyzed acylation of 2-aryloxypyridines. Geometry optimization indicates that the previously proposed intermediate, an arenium ion species as a result of analogous aromatic substitution, is not an energy minimum, but rather cationic Pt-arene η²-complex E is obtained as a stable intermediate. NEB simulations suggest that the minimum energy pathway for the acylation reaction has energy barrier of 33.6 kcal/mol and consists of the following steps: (1) Nucleophilic substitution at acetyl chloride by the platinum of the reactant A forms five-coordinate Pt(IV) acylplatinum complex B with an energy barrier of 21.7 kcal/mol. (2) B undergoes 1,2-acyl migration from the platinum to the cyclometalated carbon through a three-membered platinacycle transition state to give Pt-arene η²-complex E with an energy barrier of 14.0 kcal/mol. (3) E undergoes ligand exchange with chloride to form neutral Pt-arene η²-complex F. (4) F undergoes ligand substitution with acetonitrile to give the product and the energy barrier is small (10.6 kcal/mol). The rate-determining step is the 1,2-acyl migration step. It is interesting to note that intermediate F was not included in the proposed mechanism but was identified by the NEB simulations. Five-coordinate Pt(IV) acylplatinum complex B undergoes barrierless ligand coordination with chloride to form neutral formal oxidative addition acylplatinum complex D; however, D is less stable than reactant A by 2.9 kcal/mol, which also implies that the isolation of an oxidative addition product Pt(IV) complex may be very challenging. The direct reductive elimination of D to form product P has a higher energy barrier (36.6 kcal/mol).